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Omni-MATH / Let X be a set of 100 elements. Find the smallest possible n satisfying the following condition: Given a sequence of n subsets of X, A₁,A₂,…,A_(n), there exists 1≤i<j<k≤n such that…

Problem

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problem

Let

X

be a set of

100

elements. Find the smallest possible

n

satisfying the following condition: Given a sequence of

n

subsets of

X

A_1,A_2,\ldots,A_n

, there exists

1 \leq i < j < k \leq n

such that

A_i \subseteq A_j \subseteq A_k \text{ or } A_i \supseteq A_j \supseteq A_k.

Plain-text mathematical notation (without MathML)

Let X be a set of 100 elements. Find the smallest possible n satisfying the following condition: Given a sequence of n subsets of X, A₁,A₂,…,A_(n), there exists 1≤i<j<k≤n such that
A_(i)⊆A_(j)⊆A_(k) or A_(i)⊇A_(j)⊇A_(k).

Original LaTeX notation

Let $X$ be a set of $100$ elements. Find the smallest possible $n$ satisfying the following condition: Given a sequence of $n$ subsets of $X$, $A_1,A_2,\ldots,A_n$, there exists $1 \leq i < j < k \leq n$ such that
$$A_i \subseteq A_j \subseteq A_k \text{ or } A_i \supseteq A_j \supseteq A_k.$$

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task_id: 6c3ddb3c-69a2-50c0-bd2f-66c35ef3d438
task_key: test--6c3ddb3c-69a2-50c0-bd2f-66c35ef3d438
task_revision_id: 3
config / split: / test

Official source

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